Let $K$ be a commutative ring and $C$ be a $K$-linear category. Then $C$ is a $K$-differential algebroid if for every hom-$K$-module $Mor(a,b)$ there is a $K$-linear morphism $d_{Mor(a,b)}:Mor(a,b) \to Mor(a,b)$ such that for all objects $a,b,c\in Ob(C)$, morphisms $f:Mor(a,b)$ and $g:Mor(b,c)$, and $K$-linear morphisms $d_{Mor(a,b)}:Mor(a,b) \to Mor(a,b)$, $d_{Mor(b,c)}:Mor(b,c) \to Mor(b,c)$, and $d_{Mor(a,c)}:Mor(a,c) \to Mor(a,c)$, a generalised Leibniz rule is satisfied:

$d_{Mor(a,c)}(g \circ f) = d_{Mor(b,c)}(g) \circ f + g \circ d_{Mor(a,b)}(f)
\,.$

If all three objects are the same, this reduces down to the Leibniz rule for a derivation.